Subgroups — C₃×D₃×C₂₉×C₃₁ #30633664

Order 16182.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₂₉×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₂₉×C₃₁	—	3	1	no	maximal
4	C₃×C₂₉×C₃₁	—	2	1	no	—
5	C₃×C₂₉×C₃₁	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₂₉×C₃₁	—	3	1	no	Hall
8	C₂₉×C₃₁	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₃×C₃₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×D₃×C₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₃₁	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₂₉	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₃₁	—	3	1	no	—
14	D₃×C₃₁	C₃×C₂₉	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₂₉	—	3	1	no	—
16	D₃×C₂₉	C₃×C₃₁	1	1	yes	characteristic, direct product factor
17	C₃×C₃₁	—	2	1	no	—
18	C₃×C₃₁	D₃×C₂₉	1	1	yes	characteristic, direct product factor
19	C₃×C₃₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
20	C₃×C₂₉	—	2	1	no	—
21	C₃×C₂₉	D₃×C₃₁	1	1	yes	characteristic, direct product factor
22	C₃×C₂₉	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
23	C₂×C₃₁	—	3	1	no	Hall
24	C₂×C₂₉	—	3	1	no	Hall
25	C₃₁	C₃×D₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂₉	C₃×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃²	C₂×C₂₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	D₃	C₃×C₂₉×C₃₁	1	1	yes	characteristic, direct product factor
31	C₃	—	2	1	no	—
32	C₃	C₂×C₃×C₂₉×C₃₁	1	1	yes	characteristic, complemented
33	C₃	D₃×C₂₉×C₃₁	1	1	yes	characteristic, direct product factor
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₉×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₂₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₂₉×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₂₉×C₃₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₂₉×C₃₁	C₂	semidirect
2. D₃×C₂₉×C₃₁	C₃	direct (N × H)
5. C₃×C₂₉×C₃₁	D₃	direct (N × H)
6. C₃×C₂₉×C₃₁	C₂×C₃	semidirect
8. C₂₉×C₃₁	C₃×D₃	direct (N × H)
9. C₃×D₃×C₃₁	C₂₉	direct (N × H)
10. C₃×D₃×C₂₉	C₃₁	direct (N × H)
11. C₃²×C₃₁	C₂×C₂₉	semidirect
12. C₃²×C₂₉	C₂×C₃₁	semidirect
14. D₃×C₃₁	C₃×C₂₉	direct (N × H)
16. D₃×C₂₉	C₃×C₃₁	direct (N × H)
18. C₃×C₃₁	D₃×C₂₉	direct (N × H)
19. C₃×C₃₁	C₂×C₃×C₂₉	semidirect
21. C₃×C₂₉	D₃×C₃₁	direct (N × H)
22. C₃×C₂₉	C₂×C₃×C₃₁	semidirect
25. C₃₁	C₃×D₃×C₂₉	direct (N × H)
26. C₂₉	C₃×D₃×C₃₁	direct (N × H)
27. C₃×D₃	C₂₉×C₃₁	direct (N × H)
28. C₃²	C₂×C₂₉×C₃₁	semidirect
30. D₃	C₃×C₂₉×C₃₁	direct (N × H)
32. C₃	C₂×C₃×C₂₉×C₃₁	semidirect
33. C₃	D₃×C₂₉×C₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₂₉×C₃₁	2
D₃×C₂₉×C₃₁	3
C₂×C₃×C₂₉×C₃₁	3
C₃×D₃×C₃₁	29
C₃×D₃×C₂₉	31

Subgroups — C3×D3×C29×C31 #30633664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₂₉×C₃₁ #30633664